A mathematical explanation of Attention Mechanism
There's plenty, but keep in mind that these articles do not describe the same approach. They simply have attention shifting automation as part of their approaches and therefore must detect a need for shift and execute it in a way that improves speed, accuracy, reliability or some combination of them.

There is no one dominant attention approach and probably will not be. In fact, the earliest attention mechanism in common use in machines was likely the electromechanical fire alarm. In digital systems, it would be a vacuum tube electric eye driving an intruder alert followed by the first hardware interrupts in transistor microprocessor boards.

The sophistication of hardware interrupts in contemporary computer systems is probably higher than attention mechanisms in neural nets as of this writing, but that may change. Currently the dictionary definition of attention is the only constraint we can place on these newer approaches in artificial networks.


The four working links in the question (one is broken) lead to articles with some mathematical description, so the question half answers itself.
This article, Dynamic relevance: vision-based focus of attention using artificial neural networks,
Shumeet Baluja, Dean Pomerleau, 1995; revised 1996,
(abstract),
has only a few mathematical expressions but is filled with system
theory that could be described mathematically with a little reading
and thought.
Same with Self-Organization of an Artificial Neural Network
Subjected to Attention Shift Impairments and Familiarity
Preference, Characteristics Studied in Autism, Lennart Gustafsson and Andrew P. Papliński, 2004.
This one has clear and comprehensive mathematical treatment: Backpropagation Generalized Delta Rule for the Selective Attention Sigma-if Artificial Neural Network, Maciej Huk, 2012
This one too: Small and Dim Target Detection via Lateral Inhibition Filtering and Artificial Bee Colony Based Selective Visual Attention, Haibin Duan, Yimin Deng, Xiaohua Wang, Chunfang Xu, 2013
There is some here, but the visualizations and concepts are so theoretically relevant that one might not miss the more extensive mathematics: Using chaotic artificial neural networks to model memory in the brain, Zainab Aram, Sajad Jafari, Jun Ma, Julien C. Sprott, Sareh Zendehrouh, Viet-Thanh Pham
Solid math coverage here: Parallel Implementation of Artificial Neural Network Training, Stefano Scanzio, Sandro Cumani, Roberto Gemello, Franco Mana, P. Laface, 2010, (abstract)
Also here: Multiple Object Recognition with Visual Attention, Jimmy Lei Ba, Volodymyr Mnih, Koray Kavukcuoglu, 2015 ICLR
The mathematics for the very popular DiSAN is here: DiSAN: Directional Self-Attention Network for RNN/CNN-Free Language Understanding, Tao Shen, Jing Jiang, Tianyi Zhou, Shirui Pan, Guodong Long, Chengqi Zhang, 2018
Mathematics and the algorithm is provided for this unique approach too: Graph Classification using Structural Attention, John Boaz Lee, Ryan Rossi, Xiangnan Kong, 2018


It would be interesting to develop a taxonomy of attention approaches in AI, as that has probably not yet been done. It would take quite a study to see if any of the above bullet items match up with either of the two articles referenced in the question.